There is a very simple way to make a carbon tax progressive - in effect that is. Steal the idea behind the sky trust. Take, revenues from the carbon tax and divide them equally among the population. The result is sort of flatly progressive. The very poor receive significantly more than they pay; most of the working and middle classes get back about what they pay (some castes a bit more, some castes a bit less). The rich pay a lot more than they get back, though not in proportion to their income. So very slightly progressive, but better than extremely regressive. And in terms of winning a popular support, a whole lot better than any other type of carbon tax. You might even refer to it as a "No Hair Shirt" carbon tax.